1. Field of the Invention
The invention is directed toward systems for measuring materials properties such as strain, crystallinity, thickness, purity, composition, and the like of samples; or for observing structures in transparent materials; or, for measurement of strain in models constructed for that purpose. It is more narrowly directed toward measuring systems that utilize polarized light for such measurements. It may be used in applications including scientific research, industrial measurement, quality control, forensics, and medical imaging.
2. Description of the Related Art
Polarization interference is a well-known way to observe birefringence or retardance in a sample. Birefringence is an intensive property of a sample whereby light polarized along different axes will experience different indices of refraction. The axis along which the index is lowest is termed the fast axis, and that along which the index is highest is termed the slow axis; these are necessarily perpendicular to one another. The optical indices are termed nf and ns. Retardance R is an extensive quantity measuring the optical path difference experienced by polarized light when passing through a sample. For a uniform sample at normal incidence R=(nsxe2x88x92nf) * d, where d is the thickness of the sample.
There is a large literature describing apparatus and methods for determining the retardance of a sample. These use some form of polarized light that is either transmitted through or reflected by the sample. The change in polarization upon transmission or reflection is measured in order to determine the sample retardance. In many cases the apparatus include other optical components such as lenses that distort the polarization of light. Such polarization distortions superimpose as spurious background retardance and modify the measured sample retardance. There is a need for a method that minimizes the effect of background retardance. This is especially so for imaging systems that measure the retardance at a multitude of sample points simultaneously. In imaging systems polarization distortions typically vary from image point to image point and there are no optical methods known that can effectively compensate for the multitude of background retardance values.
Oldenbourg and Mei U.S. Pat. No. 5,521,705 teaches how to unambiguously identify the slow axis and value of R for a birefringent sample. This method uses an imaging detector and variable retarders to determine the retardance at an array of sample points. Equations for calculating retardance are given, which provide a good approximation when the retardance is less than {fraction (1/25)}th of the wavelength. Oldenbourg and Mei also show that the background retardance can successfully be separated and removed from images of samples, where the samples have small retardance magnitude values (xe2x89xa6xcex/25). For larger phase angles (xcex/24 or 15 degrees) the equations are not sufficiently accurate.
It is a goal of the present invention to obtain images of retardance R in a sample in the presence of so-called background retardance that is contributed by other components than the sample in the measuring system. By background retardance we refer to any property of optical components that alter the polarization of transmitted or reflected light, including without limitation stress birefringence and birefringent inclusions in glass, or the differential reflection or transmission of s- and p-polarized light at dielectric interfaces. It is a particular goal of the present invention to describe a background correction procedure that can be applied to larger sample retardance values (xe2x89xa72xcex/24) of up to xcex/2 and beyond, as well as to smaller values.
The invention is based on the recognition that, when measuring the retardance of a sample, the result is modified by the presence of contaminating background retardance. The measuring system usually measures a combination of the sample retardance and the apparent background retardance. We call this combination the measured sample retardance. After moving the sample out of the light path of the measuring system, the background retardance contributed by all optical elements other than the sample is determined separately. A goal of the present invention is to use the data set of the background retardance to remove it from the data set of the measured sample retardance in order to determine a more accurate value of the sample retardance, i.e. its magnitude and slow axis orientation. Since the retardance is a vector quantity, this removal is not a purely arithmetic operation.
The invention describes measurement and data analysis procedures that were developed based on the measuring system of Oldenbourg. This system employs monochromatic light with a single center wavelength. The instrument can unambiguously measure sample retardance up to half wavelength. The direction of the slow axis of the background and the sample retardance can be aligned to any direction in the image plane.
In the case that the sample retardance is larger than half wavelength, a measuring system that employs more than one center wavelength is needed to unambiguously measure sample retardance. The current invention can be applied to such systems if the multi-wavelength measurement process is performed as a sequence of single wavelength measurements, as described in the pending U.S. application Ser. No. 09/595,827 entitled xe2x80x9cPolarization Imaging Systemxe2x80x9d by Clifford Hoyt, filed Jun. 16, 2000, the entire contents of which are incorporated herein by reference.
The current invention is especially useful for imaging systems that provide an array of measurements that display the spatial distribution of sample retardance. Typically, the background retardance contributed to the sample retardance changes from point to point in the image. It is a goal of the current invention to account for this variation and correct each image point with the appropriate background retardance.
Other aspects of the invention will be apparent from the Figures and description of the preferred embodiment, which are now presented.